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Steady states and universal conductance in a quenched Luttinger model
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
Departments of Mathematics and Physics, Rutgers University.
Dipartimento di Matematica, Università degli Studi di Milano.
KTH, School of Engineering Sciences (SCI), Theoretical Physics.ORCID iD: 0000-0003-0011-2937
2016 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, p. 1-32Article in journal (Refereed) Epub ahead of print
Abstract [en]

We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian (Formula presented.) with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian (Formula presented.) which differs from (Formula presented.) by the strength of the interaction. Asymptotically in time, as (Formula presented.), after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference (Formula presented.) between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and (Formula presented.) depend on (Formula presented.) and (Formula presented.). Only for the case (Formula presented.) does (Formula presented.) equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, (Formula presented.), has a universal value equal to the conductance quantum (Formula presented.) for the spinless case.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2016. p. 1-32
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-193328DOI: 10.1007/s00220-016-2631-xISI: 000393599800005Scopus ID: 2-s2.0-84969822488OAI: oai:DiVA.org:kth-193328DiVA, id: diva2:1009221
Note

QC 20161003

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-11-20Bibliographically approved
In thesis
1. Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
Open this publication in new window or tab >>Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Recent experimental progress on ultracold atomic gases have opened up the possibility to simulate many-body systems out of equilibrium. We consider such a system described by the Luttinger model, which is a model of interacting fermions in one spatial dimension.

It is well known that the Luttinger model is exactly solvable using bosonization. This also remains true for certain extensions of the model, e.g., where, in addition, the fermions are coupled to phonons. We give a self-contained account of bosonization, together with complete proofs, and show how this can be used to solve the Luttinger model and the above fermion-phonon model rigorously.

The main focus is on non-equilibrium properties of the Luttinger model. We use the exact solution of the Luttinger model, with non-local interactions, to study the evolution starting from a non-uniform initial state with a position-dependent chemical potential. The system is shown to reach a current-carrying final steady state, in which the universal value of the electrical conductance, known from near-to-equilibrium settings, is recovered. We also study the effects of suddenly changing the interactions and show that the final state has memory of the initial state, which is, e.g., manifested by non- equilibrium exponents in its fermion two-point correlation functions.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. p. 35
Series
TRITA-FYS, ISSN 0280-316X ; 2016:59
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-193330 (URN)978-91-7729-089-6 (ISBN)
Presentation
2016-10-25, sal FB42, AlbaNova, Kungl. Tekniska högskolan, Stockholm, 15:00
Opponent
Supervisors
Note

QC 20161003

Available from: 2016-10-03 Created: 2016-09-30 Last updated: 2016-10-06Bibliographically approved
2. Non-equilibrium dynamics of exactly solvable quantum many-body systems
Open this publication in new window or tab >>Non-equilibrium dynamics of exactly solvable quantum many-body systems
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Recent experimental advances on ultracold atomic gases and trapped ions have made it possible to simulate exactly solvable quantum systems of interacting particles. In particular, the feasibility of making rapid changes, so-called quantum quenches, to such set-ups has allowed experimentalists to probe non-equilibrium phenomena in closed interacting quantum systems. This, in turn, has spurred a considerable theoretical interest in quantum many-body systems out of equilibrium.

In this thesis, we study non-equilibrium properties of quantum many-body systems in the framework of exactly solvable quantum field theory in one spatial dimension. Specific systems include interacting fermions described by the Luttinger model and effective descriptions of spin chains using conformal field theory (CFT). Special emphasis is placed on heat and charge transport, studied from the point of view of quench dynamics, and, in particular, the effects of breaking conformal symmetries on transport properties. Examples include the Luttinger model with non-local interactions, breaking Lorentz and scale invariance, and inhomogeneous CFT, which generalizes standard CFT in that the usual propagation velocity v is replaced by a function v(x) that depends smoothly on the position x, breaking translation invariance.

The quench dynamics studied here is for quantum quenches between, in general, different smooth inhomogeneous systems. An example of this is the so-called smooth-profile protocol, in which the initial state is defined by, e.g., smooth inhomogeneous profiles of inverse temperature and chemical potential, and the time evolution is governed by a homogeneous Hamiltonian. Using this protocol, we compute exact analytical results for the full time evolution of the systems mentioned above. In particular, we derive finite-time results that are universal in the sense that the same relations between the non-equilibrium dynamics and the initial profiles hold for any unitary CFT. These results also make clear that heat and charge transport in standard CFT are purely ballistic.

Finally, we propose and study an inhomogeneous CFT model with v(x) given by a random function. We argue that this model naturally emerges as an effective description of one-dimensional quantum many-body systems with certain static random impurities. Using tools from wave propagation in random media, we show that such impurities lead to normal and anomalous diffusive contributions to heat transport on top of the ballistic one known from standard CFT.

Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, 2018. p. 94
Series
TRITA-SCI-FOU ; 2018:49
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-239155 (URN)978-91-7873-032-2 (ISBN)
Public defence
2018-12-14, FD5, AlbaNova University Center, KTH Royal Institute of Technology, Stockholm, 10:00
Opponent
Supervisors
Note

QC 20181119

Available from: 2018-11-19 Created: 2018-11-16 Last updated: 2018-11-21Bibliographically approved

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